By Carolin Loos
Carolin bathrooms introduces novel ways for the research of single-cell information. either ways can be utilized to check mobile heterogeneity and hence develop a holistic figuring out of organic methods. the 1st approach, ODE limited mix modeling, allows the id of subpopulation constructions and resources of variability in single-cell picture info. the second one process estimates parameters of single-cell time-lapse facts utilizing approximate Bayesian computation and is ready to make the most the temporal cross-correlation of the information in addition to lineage info.
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Extra info for Analysis of Single-Cell Data : ODE Constrained Mixture Modeling and Approximate Bayesian Computation
The ns subpopulations with parameters ψ s and weights ws are simulated with an y external stimulus u. The multivariate mixture distribution is deﬁned by the parameters ϕs . Function h links the state vector xs of the moments of the species of the system, for which the time evolution is described by f , to the mixture parameters. For simplicity, we further neglect the subpopulation index s. 3. g. 6) or multiplicative log-normally distributed measurement noise ∼ log N (0, Γ) . 7) The entries of Γ are incorporated in the parameter vector.
A) Fitted data for Scenario 2 for both models MH1 , allowing no additional parameter variability and MH2 , which considers cell-to-cell variability in the kinetic parameters. (B) Fitted data for Scenario 3 for MH1 and MH2 . The true model MH2 has been selected correctly by AIC and BIC for both scenarios. (C, D) Proﬁles corresponding to the optimal model for Scenario 2 (C) and Scenario 3 (D). The true values of the parameters, which have been used to generate the data, are indicated by a green line.
Example. , y is proportional to the amount of xl , we obtain the mean ml and the variance Cll from the corresponding entries of the state vector of the moments. Thus, we can calculate the mean of the output my = bml and its variance Cy = b2 Cll . g. in kinetic parameters, can be incorporated. The variable parameters can be deﬁned as states and corresponding moment equations can be derived and simulated. We use normal and log-normal mixture distributions deﬁned by its mixture parameters ϕes = (μes , σse ).